96x-16x^2-64=0

Solution for 96x-16x^2-64=0 equation:

96x-16x^2-64=0

a = -16; b = 96; c = -64;
Δ = b2-4ac
Δ = 962-4·(-16)·(-64)
Δ = 5120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5120}=\sqrt{1024*5}=\sqrt{1024}*\sqrt{5}=32\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-32\sqrt{5}}{2*-16}=\frac{-96-32\sqrt{5}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+32\sqrt{5}}{2*-16}=\frac{-96+32\sqrt{5}}{-32}
$